Question

suppose that the function g is defined, for all real numbers, as follows. g(x) = { 0 if x < 0, -3 if x = 0, -1 if x > 0 } graph the function g. your answer

Explanation:

Step1: Analyze the function for \(x < 0\)

When \(x < 0\), \(g(x)=0\). This is a horizontal line along the \(x -\)axis for all negative \(x\) values.

Step2: Analyze the function for \(x = 0\)

When \(x = 0\), \(g(x)=-3\). So, we have a point \((0,-3)\)

Step3: Analyze the function for \(x>0\)

When \(x > 0\), \(g(x)=-1\). This is a horizontal line \(y = - 1\) for all positive \(x\) values.

Answer:

To graph the function \(g(x)\):

• For \(x < 0\), draw the horizontal line \(y = 0\) (but with an open - circle at \(x = 0\) since the function is not defined as \(y = 0\) at \(x=0\)).
• Plot the point \((0,-3)\).
• For \(x>0\), draw the horizontal line \(y=-1\) (with an open - circle at \(x = 0\) since the function is not defined as \(y=-1\) at \(x = 0\)).